Plethystic Murnaghan-Nakayama rule via vertex operators

Abstract

Based on the vertex operator realization of the Schur functions, a determinant-type plethystic Murnaghan--Nakayama rule is obtained and utilized to derive a general formula of the expansion coefficients of $s_{\nu }$ in the plethysm product $(p_n\circ h_k)s_{\mu }$. Meanwhile, the equivalence between our algebraic rule and the combinatorial one is also established. As an application, we provide a simple way to compute the generalized Waring formula.

16 pages, 5 figures. revised version

References in corpus (3)

• On irreducible characters of the Iwahori-Hecke algebra in type $A$
• Murnaghan-Nakayama rule and spin bitrace for the Hecke-Clifford Algebra
• A spin analog of the plethystic Murnaghan-Nakayama rule